I don't know what to say other then I'm really sorry for both of you. Perhaps, you should see a marriage counselor or therapist if only to help you deal with it... then maybe it can help you help her. Im sorry to say but I don't see how divorcing her would help anyone but you and then maybe not even that would help you since you would not be able to see the kids much if they move. And I don't see how being full time with unstable mom and the LDS church will help them. I'm sorry man that is rough.
"She was sexually abused by her father, older brother and raped as a teenager by a boyfriend twice."
That's fricken horrible man! Horrible that she had to go through that and it's horrible that she is trying to get help in things that cannot really help her. But It makes sense she has the problems you now describe. I honestly can't help but feel really sorry for her. That kind of trauma would mess anyone up.
Maybe you can reframe how you see the situation. Maybe look at it in the sense that God or destiny or the universe or whatever has put you in a position to try to help this women where basically every other man has failed her in life. She most likely clings to the LDS church because it provides stability in her world.
This may be an unpopular opinion and not what you want to hear but somethings in life are worth suffering for and through. Sometimes you don't have a choice in life but to suffer. In this case you made a choice to marry this women. If you said " in sickness and in health" then that means something. You may just need to be okay with suffering through it. That means NO ONE may ever TRULY know what it means to be her spouse and be along side her but you. And that's between you and God. If you don't believe in God then it's between you and the truth. Maybe your kids will realize it one day. Maybe not. But they need you. She needs you. If nothing other then a sense of altruism-- hold on man.
True story: My grandmother had a messed up childhood. My grandpa was the balancing and stable force in he family's he helped her stay sane. Shortly after he passed away the whole family began to realize just how much he actually did and suffered through some of her things. He didn't do it begrudgingly or ever let anyone else know what he was dealing with. Heck of a man. Heck of a legacy.